Problem: Two numbers are in the ratio of 5:6. Their sum is 77. What is the positive difference between the two numbers?
Explanation: Let $k$ be one-fifth of the smaller number, so that the two numbers are $5k$ and $6k$. Since their sum is 77, we have $5k+6k=77$, so $11k=77$, which mean $k=7$. Therefore, the difference between the numbers is $6k-5k=k=\boxed{7}$.